1992issue C011
Sizing index futures to retarget portfolio beta
A stock-index futures overlay retargets a book's market loading without rearranging the holdings. Lock the target beta, convert the gap into a listed contract count, then reconcile cash and measured return.
- Beta-hedging uses a stock-index futures overlay to raise or lower a book's market loading without rearranging the underlying holdings.
- Portfolio beta is the value-weighted average of holding betas. Cash is omitted, and the overlay notional is a beta-one sleeve equal to the futures settlement value.
- Moving a $10 million book from a beta of 1.2 to 1.4 requires a long overlay of 0.2 times that book, implemented as 13 contracts when one contract is worth $150,000.
- If margin is posted in cash, that cash draw and the full futures settlement value counted as extra equity exposure both belong in the post-overlay return.
Lock the target loading first
A stock-index futures overlay changes portfolio risk by changing the book's beta. It does that without rearranging the underlying holdings. That is the beta-hedging step: raise or lower the book's market loading with the overlay alone.
TradersWeek editorial reading: beta is a construction lever, not a forecast. Lock the target market loading first. Convert the loading gap into a listed index-future count from the contract notional. Only afterward reconcile cash and return.
What portfolio beta counts
Portfolio beta is the value-weighted average of the betas of the assets in the book. Cash is left out of that average because its beta is zero and it contributes no market loading.
Stock-index futures are treated as having a beta of one. The overlay's contribution to portfolio beta therefore equals the futures settlement value. That settlement value is the overlay notional, a beta-one sleeve added to or subtracted from the existing book.
Buying or selling the futures does not change the cost of the existing stock book. The post-overlay portfolio value used in the beta identity equals the pre-overlay stock-book value.
Turn the gap into a contract count
Futures-contract-selection is the conversion of a listed index future into a per-contract notional, so the overlay can be expressed as a whole-contract count. The listed index level and the contract multiplier set that notional.
In the worked case, moving a $10 million book from a beta of 1.2 to 1.4 requires a long overlay whose settlement value equals 0.2 times that book. With the index at 300 and a $500 multiplier, one contract is worth $150,000. The required overlay is 13.33 contracts and is implemented as 13 long contracts.
Reconcile cash and measured return
The same overlay also changes measured portfolio return, because it can alter cash balances and the amount treated as invested in equities.
If margin is posted in cash, that cash draw and the addition of the full futures settlement value to equity exposure must both be included when computing return after the overlay. That post-trade adjustment is cash-and-return-reconciliation.
The same beta identity is used to lower portfolio beta, except the overlay is sold rather than bought.
All readings on this track · 13 readings
- 1989Rank rotation opens the names; pairing keeps the hedge
- 1991Evaluating allocation sleeves against an index proxy
- 1991Construct an equity book by weakening residual co-movement, then setting a market slope
- 1992Sizing index futures to retarget portfolio beta
- 1992Portfolio beta overlays with index futures and puts
- 1997Construct a trailing stop from beta and price
- 1998An offense-defense matrix for regime-aware stock selection
- 1998Constructing a stock-book duration proxy from beta and bond markets
- 2007An index put as deductible insurance for an active stock book
- 2010Constructing option overlays for beta-adjusted portfolios
- 2014Long-only relative value with an index hedge and a crisis stop
- 2017Hedging a rising book with beta and ATR
- 2019Sizing micro index futures overlays for cash equity books